Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 1, Part B:
Comparing Number Systems (15 minutes)

How does the number system you've been working with in Part A relate to the real number system you usually use? Through analyzing a small, finite system, you've gained some understanding of number systems in general. Using units digit arithmetic, you've created an independent number system which was relatively easy to manage.

You've considered only the units digit for any one answer and in so doing have limited the size of your number system to just 10 numbers -- 0 through 9. You've seen that the finite system has its own addition and multiplication tables, additive and multiplicative inverse and identity elements, and computational rules. You've seen that the finite system does not have unique inverse elements for multiplication, as does the system of real numbers. Furthermore, you've seen that the computational rules sometimes coincide with those of the real number system. Let's explore some of the similarities and differences between the two systems.

Problem B1

 a. In what ways does addition act the same way in the finite system as it does in the infinite, real number system? Which rules are the same, and which are different? b. What about subtraction?

Problem B2

 a. In what ways does multiplication act the same way in the finite system as it does in the infinite, real number system? Which rules are the same, and which are different? b. What about division?

Problem B3

 a. Does the distributive law act the same way in the finite system as it does in the infinite, real number system? b. Why do we need a distributive law?

 Problem B4 In your opinion, what are the most important rules that apply to both this finite system and our infinite system?

 Session 1: Index | Notes | Solutions | Video